Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import math
def run():
    n=input()
    nums=[]
    for i in range(1,int(math.sqrt(2*n))+1):
        #print i
        nums.append( i* (i+1)/2)
    #print nums
    lens=len(nums)
    nums_set=set(nums)
    for i in range(lens):
        if (n - nums[i]) in nums_set:
            print "YES"
            exit()
    print "NO"

run()